Lecture_07

# Lecture_07 - PHYS 342 Fall 2010 Lecture Lecture 07 Solving...

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HYS 342 PHYS 342 Fall 2010 ecture 07: olving the Schrödinger Wave Lecture 07: Solving the Schrödinger Wave Equation in One Dimension: the Finite Square Well Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 07

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The infinite square well is sometimes o simplistic Consider the case too simplistic. when a particle of mass m is confined to a finite potential well U(x) V o x 0 L/2 -L/2
What’s Different? U(x) x E n=1 (x) 0 L/2 -L/2 U(x) V o x ? E n=1 ? 0 L/2 one click

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22 Write down the wave equation(s) 11 2 2 2 2 LL E when x mx mE      2 1 1 2 0 (1) 2 x let mE k  2 2 1 1 2 0 k x o L Ew h e n x V   2 2 2 2 2 ;( 2 ) o o mE define V EV  2 2 2 2 2 0 x
What is and E? U(x) 2 () 2 x L xC e f o r x  2 2 x L e f o r x V o E Turning points x /2 /2 0 L/2 - L/2 ) c o s ( ) L A k xf o r x 22 ( ) sin( ) e o LL xA xB k x f o r x  1 x

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Boundary Conditions Both and d 
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Lecture_07 - PHYS 342 Fall 2010 Lecture Lecture 07 Solving...

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